Question

Three weightless rods of length l each are hinged at points A and B lying on the same horizontal and joint through hinges at points C and D (Fig. 45). The length AB = 2l. A load of mass m is suspended at the hinge C.

Determine the minimum force F_min applied to the hinge D for which the middle rod remains horizontal.

Answer 1

Since the hinge C is in equilibrium, the sum of the forces applied to it is zero. 

Writing the projections of the forces (Fig. 182) acting on the hinge C on the axis perpendicular to AC, we obtain

where m_hin is the mass of the hinge. Similarly, from the equilibrium condition for the hinge D and from the condition that the middle rod is horizontal, we obtain

Solving Eqs. (1) and (2) together, we find that

Thus, the minimum force F_min for which the middle rod retains its horizontal position is

and directed at right angles to the rod BD.